1. Preheat oven to 350°. Trim ends from zucchini, but leave whole. Cook zucchini in a large saucepan of boiling salted water 3 minutes; drain and rinse under cold running water. Cut zucchini in half lengthwise. Scoop out centers to form a trench down middle of each zucchini half. Chop zucchini centers and place in a medium bowl.
2. In a medium frying pan, heat 2 tablespoons olive oil over medium heat. Add onion and cook 2 to 3 minutes, or until softened. Stir in prosciutto or ham, chopped zucchini, bread crumbs, and parsley. Cook, stirring once or twice, 2 minutes. Remove from heat and stir in 1/4 cup Parmesan cheese, egg, salt, and nutmeg.
3. Stuff zucchini with bread crumb mixture. Place zucchini in a flameproof baking dish just large enough to hold them. Drizzle remaining 1 tablespoon olive oil over zucchini and sprinkle with remaining 1/4 cup Parmesan cheese.
4. Bake 20 minutes, or until heated through. Transfer to the broiler and broil 3 inches from heat until golden brown on top, 1 to 2 minutes.